Hah, I had the same idea reading math! A different lens on a related topic is John’s post on ad hoc math definitions. In that lens, you can phrase it as: a mathematical definition that’s singled out by multiple axiomatic characterization is more likely to be “good” (natural, encompassing intuitive properties, useful in practice, appearing in multiple places, etc.). Likewise, the more obvious “prefer less axioms to more”.
An example I saw John use: Probability has multiple frameworks that each give rise to it, be it bets, theorems like complete class or savage’s theorem rooting it and expected utility in preferences, frequentism, and minimum description length/algorithmic information theory.
Hah, I had the same idea reading math! A different lens on a related topic is John’s post on ad hoc math definitions. In that lens, you can phrase it as: a mathematical definition that’s singled out by multiple axiomatic characterization is more likely to be “good” (natural, encompassing intuitive properties, useful in practice, appearing in multiple places, etc.). Likewise, the more obvious “prefer less axioms to more”.
An example I saw John use: Probability has multiple frameworks that each give rise to it, be it bets, theorems like complete class or savage’s theorem rooting it and expected utility in preferences, frequentism, and minimum description length/algorithmic information theory.